Patterns on a Roll: A Method for Continuous Feed Nanoprinting

Exploiting elastic instability in thin films has proven a robust method for creating complex patterns and structures across a wide range of lengthscales. Even the simplest of systems, an elastic membrane with a lattice of pores, under mechanical strain, generates complex patterns featuring long-range orientational order. When we promote this system to a curved surface, in particular, a cylindrical membrane, a novel set of features, patterns and broken symmetries appears. The newfound periodicity of the cylinder allows for a novel continuous method for nanoprinting.Comment: 4 pages, 4 figure

Straight Round the Twist: Frustration and Chirality in Smectics-A

Frustration is a powerful mechanism in condensed matter systems, driving both order and co plexity. In smectics, the frustration between macroscopic chirality and equally spaced layers generates textures characterised by a proliferation of defects. In this article, we study several different ground states of the chiral Landau-de Gennes free energy for a smectic liquid crystal. The standard theory finds the twist grain boundary (TGB) phase to be the ground state for chiral type II smectics. However, for very highly chiral systems, the hierarchical helical nanofilament (HN) phase can form and is stable over the TGB.Comment: 9 pages, 3 figures, submitted to J. Interface Focu

The Power of Poincar\'e: Elucidating the Hidden Symmetries in Focal Conic Domains

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincar\'e symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.Comment: 4 pages, 3 included figure

Helical Nanofilaments and the High Chiralty Limit of Smectics A

Liquid crystalline systems exhibiting both macroscopic chirality and smectic order experience frustration resulting in mesophases possessing complex three-dimensional order. In the twist-grainboundary phase, defect lattices mediate the propagation of twist throughout the system. We propose a new chiral smectic structure composed of a lattice of chiral bundles as a model of the helical nanofilament (B4) phase of bent-core smectics

Smectic Pores and Defect Cores

Riemann's minimal surfaces are a complete, embeddable, one-parameter family of minimal surfaces with translational symmetry along one direction. It's infinite number of planar ends are joined together by an array of necks, closely matching the morphology of a bicontinuous, lamellar system with pores connecting alternating layers. We demonstrate explicitly that Riemann's minimal surfaces are composed of a nonlinear sum of two oppositely-handed helicoids. This description is particularly appropriate for describing smectic liquid crystals containing two screw dislocations.Comment: 6 pages, 4 figures, Geometry of Interfaces Oct 2011, Primosten, Croati

Elastic Instability Triggered Pattern Formation

Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a "dislocation dipole" located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.Comment: 15 pages, 7 figures, the full catastroph

Colloquium : disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet

Self-assembly of twisted, multi-sheet aggregates

Hierarchical self-assembly underpins much of the diversity of form and function seen in soft systems, yet the pathways by which they achieve their final form are not always straightforward – intermediate steps, kinetic effects and finite sizes of aggregates all influence the self-assembly pathways of these systems. In this paper, we use molecular dynamics simulations of binary mixtures of spheres and ellipsoidal discs to investigate the self-assembly of anisotropic aggregates with internal structures. Through this, the full aggregation pathways of spontaneously chiral, multi-bilayer and multi-layer assemblies have been tracked and characterised via a semi-qualitative analysis. This includes the unambiguous identification of first-, second- and third-generation hierarchical assemblies within a single simulation. Given the significant challenge of tracking full aggregation pathways in experimental systems, our findings strongly support the notion that molecular simulation has much to contribute to improving our understanding of hierarchical self-assembling systems

Helical Nanofilaments and the High Chirality Limit of Smectics-A

Liquid crystalline systems exhibiting both macroscopic chirality and smectic order experience frustration resulting in mesophases possessing complex three-dimensional order. In the twist-grain-boundary phase, defect lattices mediate the propagation of twist throughout the system. We propose a new chiral smectic structure composed of a lattice of chiral bundles as a model of the helical nanofilament (B4) phase of bent core smectics.Comment: 4 pages, 3 figures, the full catastroph